Find the term independent of x in \((x^3 - \frac{3}{x^2})^{15}\)

1.	Find the term independent of x in \((x^3 - \frac{3}{x^2})^{15}\)
Answer» \((x^3 - \frac{3}{x^2})^{15}\) Here x → x³, a = \((\frac{-3}{x^2})^r\) and n = 15 T_r+1 = ¹⁵C_r.(x³)^{15- r} \((\frac{-3}{x^2})^r\). = ¹⁵C_r.x^45-r.x^-2r (-3)^r = ¹⁵Cr.(-3)^r .x^45-5r To find the term independent of x we have 45 – 5r = 0 :. 45 = 5r ⇒ r = 9 T₉₊₁ = ¹⁵C₉.(-3)⁹ .x⁰ T₁₀= ^-15C₉.(3)⁹ is the term independent of x.

Answer»

\((x^3 - \frac{3}{x^2})^{15}\)

Here x → x³, a = \((\frac{-3}{x^2})^r\) and n = 15

T_r+1 = ¹⁵C_r.(x³)^{15- r} \((\frac{-3}{x^2})^r\).

= ¹⁵C_r.x^45-r.x^-2r (-3)^r

= ¹⁵Cr.(-3)^r .x^45-5r

To find the term independent of x we have 45 – 5r = 0

:. 45 = 5r ⇒ r = 9

T₉₊₁ = ¹⁵C₉.(-3)⁹ .x⁰

T₁₀= ^-15C₉.(3)⁹ is the term independent of x.

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